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Recognition Using Region Correspondences
 International Journal of Computer Vision
, 1995
"... A central problem in object recognition is to determine the transformation that relates the model to the image, given some partial correspondence between the two. This is useful in determining whether an object is present in an image, and if so, determining where the object is. We present a novel me ..."
Abstract

Cited by 34 (7 self)
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A central problem in object recognition is to determine the transformation that relates the model to the image, given some partial correspondence between the two. This is useful in determining whether an object is present in an image, and if so, determining where the object is. We present a novel method of solving this problem that uses region information. In our approach the model is divided into volumes, and the image is divided into regions. Given a match between subsets of volumes and regions (without any explicit correspondence between different pieces of the regions) the alignment transformation is computed. The method applies to planar objects under similarity, affine, and projective transformations and to projections of 3D objects undergoing affine and projective transformations. 1 Introduction A fundamental problem in recognition is pose estimation. Given a correspondence between some portions of an object model and some portions of an image, determine the transformation th...
Paraperspective ... Affine
, 1994
"... It is shown that the set of all paraperspective images with arbitrary reference point and the set of affine images of a 3D object are identical. Consequently, all uncalibrated paraperspective images of an object can be constructed from a 3D model of the object by applying an affine transformation ..."
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Cited by 8 (5 self)
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It is shown that the set of all paraperspective images with arbitrary reference point and the set of affine images of a 3D object are identical. Consequently, all uncalibrated paraperspective images of an object can be constructed from a 3D model of the object by applying an affine transformation to the model and every affine image of the object represents some uncalibrated paraperspective image of the object. It follows that the paraperspective images of an object can be expressed as linear combinations of any two nondegenerate images of the object. When the image position of the reference point is given the parameters of the affine transformation (and, likewise, the coefficients of the linear combinations) satisfy two quadratic constraints. Conversely, when the values of parameters are given the image position of the reference point is determined by solving a biquadratic equation.
Indexing Based on Algebraic Functions of Views
 COMPUTER VISION AND IMAGE UNDERSTANDING
, 1998
"... this paper, we propose the use of algebraic functions of views for indexingbased object recognition. During indexing, we consider groups of model points and we represent all the views (i.e., images) that they can produce in a hash table. The images that a group of model points can produce are compu ..."
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Cited by 6 (5 self)
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this paper, we propose the use of algebraic functions of views for indexingbased object recognition. During indexing, we consider groups of model points and we represent all the views (i.e., images) that they can produce in a hash table. The images that a group of model points can produce are computed by combining a small number of reference views which contain the group using algebraic functions of views. Fundamental to this procedure is a methodology, based on Singular Value Decomposition and Interval Arithmetic, for estimating the allowable ranges of values that the parameters of algebraic functions can assume. During recognition, scene groups are used to retrieve from the hash table the most feasible model groups that might have produced the scene groups. The use of algebraic functions of views for indexingbased recognition offers a number of advantages. First of all, the hash table can be built using a small number of reference views per object. This is in contrast to current approaches which build the hash table using either a large number of reference views or 3D models. Most importantly, recognition does not rely on the similarity between reference views and novel views; all that is required for the novel views is to contain common groups of points with a small number of reference views. Second, verification becomes simpler. This is because candidate models can now be backprojected onto the scene by applying a linear transformationona small number of reference views of the candidate model. Finally, the proposed approach is more general and extendible. This is because algebraic functions of views have been shown to exist over a wide range of transformations and projections. The recognition performance of the proposed approach is demonstrated using both artific...
3D to 2D Recognition with Regions
 IEEE Conference on Computer Vision and Pattern Recognition
, 1997
"... This paper presents a novel approach to partsbased object recognition in the presence of occlusion. We focus on the problem of determining the pose of a 3D object from a single 2D image when convex parts of the object have been matched to corresponding regions in the image. We consider three t ..."
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Cited by 3 (0 self)
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This paper presents a novel approach to partsbased object recognition in the presence of occlusion. We focus on the problem of determining the pose of a 3D object from a single 2D image when convex parts of the object have been matched to corresponding regions in the image. We consider three types of occlusions: selfocclusion, occlusions whose locus is identified in the image, and completely arbitrary occlusions. We derive efficient algorithms for the first two cases, and characterize their performance. For the last case, we prove that the problem of finding valid poses is computationally hard, but provide an efficient, approximate algorithm. This work generalizes our previous work on regionbased object recognition, which focused on the case of planar models. A preliminary version of this paper has appeared in [29] A brief overview of these and related results has appeared in [8] y This research was supported by the Unites StatesIsrael Binational Science Foundation, Gr...
unknown title
"... It is shown that the set of all paraperspective images with arbitrary reference point and the set of all affine images of a 3D object are identical. Consequently, all uncalibrated paraperspective images of an object can be constructed from a 3D model of the object by applying an affine transformat ..."
Abstract
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It is shown that the set of all paraperspective images with arbitrary reference point and the set of all affine images of a 3D object are identical. Consequently, all uncalibrated paraperspective images of an object can be constructed from a 3D model of the object by applying an affine transformation to the model, and every affine image of the object represents some uncalibrated paraperspective image of the object. It follows that the paraperspective images of an object can be expressed as linear combinations of any two nondegenerate images of the object. When the image position of the reference point is given the parameters of the affine transformation (and, likewise, the coefficients of the linear combinations) satisfy two quadratic constraints. Conversely, when the values of parameters are given the image position of the reference point is determined by solving a biquadratic equation. Key words: affine transformations, calibration, linear combinations, paraperspective projection, It is shown below that given an object O ⊂ R3, the set of all images of O obtained by applying